Details

analyze1.9s (19.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample97.0ms (1%)

Algorithm

1×

intervals

Results

45.0ms	115×	body	1024	valid
23.0ms	39×	body	2048	valid
10.0ms	47×	body	512	valid
5.0ms	36×	body	128	valid
3.0ms	19×	body	256	valid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

39.3b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	39.3b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.0b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.6b	(tan.f64 (+.f64 x eps))

rewrite116.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

22.7b

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 43

Calls

2 calls:

6.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 815 to 169 computations (79.3% saved)

series99.0ms (1%)

Error

13.3b

Counts

2 → 24

Calls

2 calls:

43.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
30.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 1685 to 1001 computations (40.6% saved)

simplify113.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

936×	`fma-def_binary64`
909×	`times-frac_binary64`
194×	`associate-+r+_binary64`
142×	`unswap-sqr_binary64`
125×	`+-commutative_binary64`

Counts

67 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	207	2114
1	507	1833
2	1787	1692
3	4965	1689
4	4986	1689
5	4943	1689

prune58.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	4	48

Error

0.3b

Counts

48 → 4

Alt Table

Status	Error	Program
	40.9b	(-.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 (cos.f64 eps) 2)) x (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (.f64 x x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 eps) 2) (pow.f64 x 3)) (pow.f64 (cos.f64 eps) 2)) (+.f64 (fma.f64 (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 3)) (.f64 x x) x) (.f64 (pow.f64 x 3) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) 4) (pow.f64 (cos.f64 eps) 4)) 1/3))))) (tan.f64 x))
▶	23.3b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	32.3b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	32.3b	(+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (.f64 (/.f64 (.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))

Compiler

Compiled 1424 to 666 computations (53.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))
7.6b	(fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))))

rewrite207.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`associate-r_binary64`
10×	`tan-quot_binary64`
10×	`add-cube-cbrt_binary64`

Counts

4 → 82

Calls

4 calls:

8.0ms	(*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))
8.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
1.0ms	(fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))))

Compiler

Compiled 2712 to 713 computations (73.7% saved)

series327.0ms (3.4%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

91.0ms	(fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))))
78.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
43.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
38.0ms	(*.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))

Compiler

Compiled 4265 to 2183 computations (48.8% saved)

simplify272.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-def_binary64`
395×	`associate-/l*_binary64`
368×	`times-frac_binary64`
250×	`distribute-rgt-in_binary64`
238×	`distribute-lft-in_binary64`

Counts

130 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	2939
1	622	2732
2	2002	2667
3	4780	2667
4	4890	2667
5	5091	2667

prune141.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	8	77
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	71	10	81

Error

0.1b

Counts

81 → 10

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	32.3b	(+.f64 (+.f64 eps (+.f64 (/.f64 (pow.f64 eps 3) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 4)) (fma.f64 5/3 (/.f64 (pow.f64 eps 4) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3)) (fma.f64 (/.f64 (pow.f64 eps 4) (pow.f64 (cos.f64 x) 5)) (pow.f64 (sin.f64 x) 5) (fma.f64 4/3 (/.f64 (.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 eps 3)) (pow.f64 (cos.f64 x) 2)) (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) (fma.f64 1/3 (pow.f64 eps 3) (.f64 2/3 (.f64 (/.f64 (sin.f64 x) (cos.f64 x)) (pow.f64 eps 4)))))))))) (.f64 (/.f64 (*.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))
	23.3b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (+.f64 (.f64 (cos.f64 x) (tan.f64 x)) (.f64 (cos.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	23.9b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 eps) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps))))) (cbrt.f64 (fma.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 eps) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))))) (cbrt.f64 (fma.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 eps) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	26.0b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 eps) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) 3)) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	23.4b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (.f64 (cbrt.f64 (tan.f64 x)) (cbrt.f64 (tan.f64 x))) (.f64 (tan.f64 eps) (cbrt.f64 (tan.f64 x)))) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	24.8b	(/.f64 (log1p.f64 (expm1.f64 (fma.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 eps) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	23.4b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (cos.f64 x) (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (sin.f64 x) (cos.f64 x))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	23.5b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (.f64 (.f64 (cbrt.f64 (cos.f64 x)) (cbrt.f64 (cos.f64 x))) (.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cbrt.f64 (cos.f64 x))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	32.3b	(+.f64 (fma.f64 eps (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) eps) (.f64 (/.f64 (.f64 eps eps) (cos.f64 x)) (+.f64 (sin.f64 x) (/.f64 (pow.f64 (sin.f64 x) 3) (pow.f64 (cos.f64 x) 2)))))

Compiler

Compiled 3238 to 1238 computations (61.8% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
0.3b	(pow.f64 (sin.f64 x) 2)

rewrite405.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

33×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`associate-l_binary64`

Counts

4 → 118

Calls

4 calls:

32.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))
16.0ms	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 4444 to 1652 computations (62.8% saved)

series319.0ms (3.3%)

Error

0.1b

Counts

4 → 42

Calls

4 calls:

162.0ms	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
57.0ms	(*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))
39.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
22.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 3610 to 2032 computations (43.7% saved)

simplify205.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

334×	`times-frac_binary64`
292×	`associate-/l*_binary64`
267×	`associate-r_binary64`
266×	`associate-l_binary64`
190×	`fma-def_binary64`

Counts

160 → 118

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	408	5818
1	1226	4944
2	4684	4932
3	4999	4932
4	4999	4932
5	4990	4932

prune174.0ms (1.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	10	118
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	116	12	128

Error

0.0b

Counts

128 → 12

Alt Table

Status	Error	Program
	1.4b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 eps)) (cbrt.f64 (sin.f64 eps))) 1) (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (cbrt.f64 (sin.f64 eps)) (cos.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	10.9b	(expm1.f64 (log1p.f64 (/.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))))
	1.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (cbrt.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps))))) (cbrt.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.5b	(/.f64 1 (/.f64 (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps)))))
	23.3b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (+.f64 (.f64 (cos.f64 x) (tan.f64 x)) (.f64 (cos.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	19.2b	(cbrt.f64 (pow.f64 (/.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))) 3))
	26.0b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 eps) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) 3)) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.5b	(/.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 (cos.f64 x) (/.f64 (cbrt.f64 (pow.f64 (pow.f64 (sin.f64 x) 2) 3)) (cos.f64 x)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.6b	(/.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 (pow.f64 (cos.f64 x) 2) (/.f64 (/.f64 (pow.f64 (sin.f64 x) 4) (cos.f64 x)) (cos.f64 x)))) (.f64 (cos.f64 eps) (-.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	32.3b	(+.f64 (/.f64 eps (/.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3) eps)) (+.f64 (/.f64 (.f64 (sin.f64 x) (.f64 eps eps)) (cos.f64 x)) (+.f64 eps (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) eps) (pow.f64 (cos.f64 x) 2)))))
	0.5b	(/.f64 (.f64 (sin.f64 eps) (+.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) 3))) (.f64 (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 eps) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (cos.f64 x)) (pow.f64 (cos.f64 x) 2)))))
▶	0.4b	(.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))

Compiler

Compiled 4210 to 1855 computations (55.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps)))
0.3b	(pow.f64 (sin.f64 x) 2)

rewrite206.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

33×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
27×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
21×	`associate-r_binary64`

Counts

4 → 121

Calls

4 calls:

19.0ms	(.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
5.0ms	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps)))
4.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
2.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 4356 to 1492 computations (65.7% saved)

series246.0ms (2.5%)

Error

0.0b

Counts

4 → 42

Calls

4 calls:

120.0ms	(.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
36.0ms	(/.f64 (sin.f64 eps) (*.f64 (cos.f64 x) (cos.f64 eps)))
36.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
9.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 3494 to 1940 computations (44.5% saved)

simplify128.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
287×	`unswap-sqr_binary64`
230×	`associate-l_binary64`
229×	`associate-/l*_binary64`
226×	`associate-r_binary64`

Counts

163 → 90

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	387	5540
1	1041	4780
2	3832	4727
3	5236	4727

prune93.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	91	11	102

Error

0.0b

Counts

102 → 11

Alt Table

Status	Error	Program
	26.0b	(/.f64 (cbrt.f64 (pow.f64 (fma.f64 (sin.f64 x) (fma.f64 (tan.f64 x) (tan.f64 eps) -1) (.f64 (cos.f64 x) (+.f64 (tan.f64 x) (tan.f64 eps)))) 3)) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.5b	(.f64 (/.f64 1 (/.f64 (cos.f64 x) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (/.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	1.4b	(/.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (sin.f64 eps)) (cbrt.f64 (sin.f64 eps))) 1) (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (cbrt.f64 (sin.f64 eps)) (cos.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	10.9b	(expm1.f64 (log1p.f64 (/.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))))
	23.3b	(/.f64 (fma.f64 (sin.f64 x) (+.f64 (.f64 (tan.f64 x) (tan.f64 eps)) -1) (+.f64 (.f64 (cos.f64 x) (tan.f64 x)) (.f64 (cos.f64 x) (tan.f64 eps)))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.4b	(.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (cos.f64 eps))) (/.f64 (+.f64 (cos.f64 x) (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 6)) (cos.f64 x))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.8b	(.f64 (.f64 (/.f64 (sin.f64 eps) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (cbrt.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (cbrt.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))))) (/.f64 (cbrt.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)))) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))
	0.6b	(/.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 (pow.f64 (cos.f64 x) 2) (/.f64 (/.f64 (pow.f64 (sin.f64 x) 4) (cos.f64 x)) (cos.f64 x)))) (.f64 (cos.f64 eps) (-.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))) (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
	32.3b	(+.f64 (/.f64 eps (/.f64 (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) 3) eps)) (+.f64 (/.f64 (.f64 (sin.f64 x) (.f64 eps eps)) (cos.f64 x)) (+.f64 eps (/.f64 (*.f64 (pow.f64 (sin.f64 x) 2) eps) (pow.f64 (cos.f64 x) 2)))))
	0.5b	(/.f64 (.f64 (sin.f64 eps) (+.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) 3))) (.f64 (.f64 (cos.f64 x) (-.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))) (*.f64 (cos.f64 eps) (fma.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (-.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x)) (cos.f64 x)) (pow.f64 (cos.f64 x) 2)))))
	1.5b	(/.f64 (.f64 (.f64 (cbrt.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) (cbrt.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps))))) (cbrt.f64 (.f64 (+.f64 (cos.f64 x) (/.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))) (/.f64 (sin.f64 eps) (cos.f64 eps))))) (.f64 (cos.f64 x) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))))

Compiler

Compiled 2491 to 1053 computations (57.7% saved)

regimes1.7s (17.1%)

Accuracy

Total 0.4b remaining (87.3%)

Threshold costs 0.4b (87.3%)

Compiler

Compiled 38860 to 22415 computations (42.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	49
1	31	49
2	35	49
3	37	49
4	38	49
5	37	49

end1.0ms (0%)

Compiler: Compiled 32 to 22 computations (31.3% saved)

sample2.9s (29.9%)

Algorithm

1×

intervals

Results

1.0s	3410×	body	1024	valid
716.0ms	1279×	body	2048	valid
359.0ms	1390×	body	512	valid
149.0ms	1309×	body	128	valid
83.0ms	609×	body	256	valid
3.0ms	3×	body	4096	valid

Compiler

Compiled 501 to 301 computations (39.9% saved)

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11

Details

analyze1.9s (19.1%)

sample97.0ms (1%)

simplify14.0ms (0.1%)

prune1.0ms (0%)

localize6.0ms (0.1%)

rewrite116.0ms (1.2%)

series99.0ms (1%)

simplify113.0ms (1.2%)

prune58.0ms (0.6%)

localize21.0ms (0.2%)

rewrite207.0ms (2.1%)

series327.0ms (3.4%)

simplify272.0ms (2.8%)

prune141.0ms (1.5%)

localize27.0ms (0.3%)

rewrite405.0ms (4.2%)

series319.0ms (3.3%)

simplify205.0ms (2.1%)

prune174.0ms (1.8%)

localize20.0ms (0.2%)

rewrite206.0ms (2.1%)

series246.0ms (2.5%)

simplify128.0ms (1.3%)

prune93.0ms (1%)

regimes1.7s (17.1%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.9s (29.9%)

Profiling

Iter	Nodes	Cost
0	7	11
1	10	11
2	15	11
3	22	11
4	29	11
5	46	11
6	72	11
7	93	11
8	110	11
9	120	11
10	124	11
11	126	11
12	112	11